Thursday, January 9, 2014

"Let none be ashamed to learn, for a good work requireth good counsel."

- Albrecht Dürer, 1520

Mathematics and Art, sometimes thought to be opposite poles of human experience and activity, can sometimes sit down together in conversation.

Sometimes we might think of the conversation as more of a lecture - with Mathematics providing some technical advice. Perspective drawing is the prime example - where mathematics allows artists to create realistic images, or else to subvert the expectations of realism (as in anamorphic art). Art does reply - for these mathematical tools, it repays the favor by providing Mathematics with inspiring teaching and learning opportunities (in the case perspective drawing, see this essay by mathematician Annalisa Crannell).

Art may ask questions of Mathematics - after all, math is not merely a tool; it's often the inspiration for Art's work. Geometry, often in the form of polygons, polyhedra, and tessellations, makes many appearances in art from the old (see for example the work of Albrecht Druer, or this essay on Raphael's famous painting The School of Athens), to the new (check out the latest Bridges mathematical art galleries). Art that springs from Math can, in turn, say something back to Math - providing motivation in math education (see most posts from mathmunch), and inspiration for working mathematicians. A big part of what gets me excited about the recreational math that I do are the pretty pictures (I've been putting pictures from this blog that I like over on this tumblr for a while).

The book Beautiful Geometry gives us a rare opportunity to listen in on an extended and fascinating dialog between Math and Art: here they are talking like old friends, sharing jokes, and discussing other subjects like history and literature through the pairing of brief and interesting essays by mathematician Eli Maor and beautiful illustrations by artist Eugen Jost.

You will likely want to join in the conversation - the essays and artwork in Beautiful Geometry are inspiring and motivating - prompting me, at least, to try to play around with their ideas. For example, the images below are from a Geometer's Sketchpad iteration based on Jost's artwork entitled 3/3 = 4/4, which accompanies Maor's essay on geometric series (Chapter 30).

These images represent some early partial sums of the series below - can you see how?

Although some of Jost's pieces allow themselves to be mimicked by us amateurs (armed with appropriate software), many are true art works, conveying an aesthetic that keeps them from being mere diagrams (while still saying something substantive about mathematics).

Several of the topics that Maor writes about are ones I've looked at before (Lissajous figures, means, hypocycloids, figurate numbers), but even in these somewhat familiar areas the essays and illustrations are nudging me to look back and explore some more. (I even learned something new about quadrilaterals: connecting the midpoints of a quadrilateral always yields a parallelogram - Chapter 3).

Jost's art and Maor's articles are going to inspire many of us to continue experiencing mathematics through beauty, and to look at art with a greater understanding of the math that helps to make it beautiful.